All lamps are not equal.
You're safe with genuine Philips or Osram. When supplied new, your projector will have been fitted with one or the other brand. They are of equal quality. 3rd party lamp "compatible" lamps are something of lottery.
At the better end you have Diamond lamps. These are generally as bright as a genuine Philips/Osram and maintain their brightness about as well as an original over the lamp's life. Colour quality is decent too. They're cheaper, but if there's a catch it's the consistency. There are reports of new Diamond lamps being duller than the old lamp they're replacing. A return/replacement generally solves it, but it's a hassle if you get a bad 'un.
All other 3rd party lamps is wild west time. Some are about 70-80% of the original brightness, but dim or fail quickly. Others just look dull immediately and lose their remaining brightness in 1/4 to 1/2 of the typical life span. Cheap, but TBH, they're a false economy.
The other thing to be aware of is the crappy lamps can put a bit of strain on the lamp ballast circuit because they need a bigger start voltage to strike up. Quite a few JVC projector owners have come a cropper because of this. I haven't heard the same about Optoma though.
One useful way to save money relatively safely is to buy a bare lamp. What I mean is that when you take the lamp out of the projector, you're really removing a two-piece component; there's the lamp, and the housing for the lamp. It's possible to remove the lamp from the housing, then use a new lamp in the original housing.
Wherever you buy from, make sure you're buying a genuine Philips or Osram lamp. There should be markings with the part number on the bell of the original. Use that as a guide.