Both are less than good, with the BEC being utter crap 99% of the time. Also, as a general rule, the greater the magnification, the higher quality glass you require, the worse the budget scopes are gonna be.
I've used a 10x scope to spot .308 holes at 200 yards without too much problem. Bushnell 3200 is a good suggestion, and (I know this goes against what I said before) but a used Tasco Super Sniper 10x might be within your budget.
Another option (and I HATE MYSELF for doing this, because it always bugs me when people do it) BUT if you could wait a TAD longer and save another $50, the Burris Fullfield II is a very good quality optic for the money. The 3-9x40 model comes with a FREE 20x spotting scope that can easily see .223 caliber holes at 200 yards, so .308 at 300 shouldn't be too bad. As another bonus, the Fullfield II has the "Ballistic Plex" with additional lines at 200 - 500 yards, so you just sight in, hold over, and shoot. It's a sweet scope and spotter for a mere $199.