Question....I shoot baseball for a hobby and need to get out as cheap as possible. Should I upgrade my lens for my Canon Rebel T3i or purchase a 90D?
I am not able to upgrade camera and lens at the same time. I'm not even sure if there is another lens that would fit the Rebel.
I currently use the EF 75-300mm 1:4-5.6 III and my images are just not as crisp as I'd like.
What are your shooting conditions? Can you post a link to an actual file(s) on Dropbox or One Drive?
If you are sure the problem is the lens, and not technique, look into the EF-S 55-250mm STM lens.
A little less reach than your 300mm lens, but it is a sharp lens and you will be able to crop a little if you aren't close enough.
Over the years, we've used all of the 75-300 series lenses that came either in a kit or as a bonus with various cameras. Although I gave them a go, I never liked any of them for basically the same reason you state. We already had the first iteration of the EF 70-300mm f/4-5.6 IS USM and the EF 70-300mm f/4-5.6 L IS USM which we used on Rebels, XSi and T4i, so I had a good opportunity to compare the lenses.
Since at this time you either want new glass or new camera, IMHO your best move is glass. You will see a world of difference with either Johns suggestion of the EF-S 50-250mm f/4-5.6 IS STM or for less than $200 more the EF 70-300mm f/4-5.6 IS nano USM mark II. Both are available refurbished at the Canon Store. I have never used the 50-250mm because I've always had that range covered with the 70-300's, but it gets very good reviews. However, we have used or just tested the 70-300 mark II on the T4i, t6s, T7i, 70D, 7D mark II, 5D mark IV, R5, and R6 (with adapter) and the IQ of this lens improves with each move, not "L" quality, but dang impressive for the price range. My point is, this lens will keep up as you move up in cameras, so it is an investment until you can get into L glass and better cameras.
"Should I upgrade my lens for my Canon Rebel T3i or purchase a 90D?"
It almost always, 90% of the time best to buy a better lens than a better camera. Your delima is the 90D is a much better camera, Way better in every aspect. It is not likely to get real noticeably better sports shots if you have to use your current lenses though.
I don't know what your budget looks like but if I truly wanted to get great sports pictures I would buy one of the 150-600mm super zooms. If new is out of the budget they are a good candidate on the used market. You can find used ones that got very little use because they are a limited use lens. But they excel at sports and wildlife shots. All of them currently available are very sharp. Even the older discontinued models like the 150-500mm zooms are very good. They can be had pretty inexpensively.
The good thing about your Rebel is almost all Canon lenses will fit and work as long as it says EF-S or EF in its name. All the super zoom off brand lenses will work beautifly.
You might want to look at a monopod if you get a 150-600mm super zoom. I don't usually use one or need it but some guys like them.
If you buy the EF-S 55-250mm STM lens which is a much better lens than what you have but almost any lens is better than what you have, you will lose 50mm. Not a big deal but nobody wants to give up FL. Plus is is still in the same class of lens as you have. The 150-600mm super zooms are a big step up improvement.
Newton gave a very good account of the option, and Ernie has given some great choices too. Personally, I think in terms of cost/benefit that if you are happy with the focal range of your 75-300, then EF 70-300 would be the way to go. It covers from reasonably close to a decent distance. I enclose a link to a post on this site for my review and samples of the EF 70-300 lens range for your information HERE . I don't shoot baseball but I do shoot wildlife, which has some commonalities.
I love the 150-600 range - I use it for wildlife, but it will be more expensive, and significantly heavier and more unwieldy, and you lose a lot of focal range at the wider angle: which may not be an issue, depending upon your location. Still, the 70-300 range will be useful in all sorts of other occasions when the larger, heavier super tele lenses will not be suitable.
"... you lose a lot of focal range at the wider angle: which may not be an issue, depending upon your location."
I would venture a guess that most guys are at the long end of a tele zoom lens way more often than at the short end. The loss on the short end will be almost unnoticed but the up to 600mm on the long end when you need it is priceless. I'll bet I haven't shot a dozen pictures with my 150-600mm Sport zoom at 150mm side since I've had it.
It's just something you don't do when you are needing a tele whether it is the 70-300mm or a 150-600mm. IMHO, I would prefer a 300mm or 400mm prime lens to the 70-300mm zoom especially if I am shooting sports or wildlife.
Like I said if the price is not possible right now check the used market. A 150-600mm super zoom is not a lens that most of use ever wear out. Plus all of them are well built. People buy them for the high school years and when that is done they have little use for one so it sits or gets sold. Usually still in very good shape. Perhaps that may even be you!
Ernie makes some good points as regards focal length and I agree with much he says. My reasons for suggesting the 70-300 range were for budget and the weight of the lens - in the end you can get only what you can afford and are prepared to carry.
As I said, I love the 150-600mm range and it would be the way to go if you can afford it. There are some deals to be had on the used market, you just have to be careful about where, and from whom you purchase. If you had the budget, and wanted one lens to do it all the Sigma 60-600 OS USM lens is a stunning unit, with great optics and stabilization, but pricey and heavy.
As to the choice between fixed and zoom. To me, a lot depends on what you are going to produce: which, in the end, is what it is all about. The requirements for large, details prints are different from producing small print or for digital display for for the web, which images are often downsized in any case.
A benefit of a prime lens should deliver better image quality, however the down side is that you are limited in your ability to frame the subject because you can't zoom to do so. It's not an issue if your subject are all in the midfield, for example, but may render challenges if you are switching between that and the batting area and then the outfield. So, much depends on where and how you shoot, and none of us can predict that precisely.
My reasons for suggesting the 70-300mm II are from personal experience and I can relate to the OP's situation, I've been there when I first started shooting. The OP seems happy with the FL with the exception of the poor quality of the 75-300mm III, which we all are of the opinion isn't Canons best effort. Typically, I would take my camera and one lens to local events, which seems to be what the OP is doing, and the 70-300 proved to be the most versatile focal range. I could shoot some near WA shots (70mm) when I needed it or zoom to 300mm when needed and anything in between. Many shots that I took would simply not have been possible with a 150-600. Yes, I used the 70-300mm L on my T4i, but the 70-300mm mark II with it's updated glass, great IS, and lighter weight are up to the task and easy to lug around. I owned the 150-600 and just didn't like the heft, and I suspect the OP would feel the same putting this hefty lens on a T3i.
Absolutely agree that we have to go with the needs, constraints, and desires of the person seeking assistance. In this case, I certainly respect theOP's budget and, as you say, they seem comfortable with the focal length and weight of a unit like the 70-300. I have all of the 70-300 lens models except the DO version that is both expensive and not necessarily a great lens. The EF 70-300 IS USM MkII is a great lens, as we agree.
We can only give advice based on our understanding of the OP's needs, the rest will be up to them...
As I said, I don't shoot baseball, but I do recognize that there are elements across a wide range of focal lengths