What's the longest distance you're going to shoot?
If you're limited on funds, then I'm presuming that you only want to stick with a stock rifle?
IF you're shooting at 300 yards or so and under, then I'd say either one will do. You will spending more on powder to reload .22-250, but I don't know just how much penny pinching you're doing. Everything else is equal.
Twist rate on your rifle at this point shouldn't be an issue. 52gr SMK HPBT works great in my rifle's 1:12 twist. chambered in .22-250. The .223 will match the .22-250 in performance at this range.
IF you're shooting at 400+ yards, this is where I think the .22-250 starts to outperform the .223. I'd recommend both of these cartridges to be used with a faster twist rate such as 1:8 and heavier bullets (or at least a longer ogive). In order to maximize either one, you'll need the heavier bullet to buck the wind and faster twist rate to keep it stabilized. Don't get me wrong, the .223 has potential at up to 600 yards, but you'll be taking a little greater effort and time to match the .22-250.
IF you're wanting to go longer than 600 yards, I don't recommend either one. I think you need to reconsider your choices because there's simply better cartidges that will leave both of these in the dust at this range...
Like Scorch said: If noise is a factor at your range, the .223 is a little "quieter", but not that much IMO.
plus the 22-250 burns out the bbls fairly quickly.
In general terms, I have to agree with this statement. However, two items to consider:
1. How many rounds/year are you considering firing? If you're in the neighborhood of 500-1000, then (depending on brand you select) you may end up changing barrels every 2-3 years. If you're not, I think the rifle will last for years before worrying about this issue.
2. If you are considering .22-250 even though you're planning to shoot that much, I HIGHLY recommend buying a Savage. The reasons are they are about the most accurate rifle out-of-the-box out there with a price tag that won't make your jaw drop to the floor. And the barrels are easy to change out. By then, you can afford to attach another brand if you wish without knowing brain surgery.
Just my thought on the issue...