In reply to AndrewB121:
Is it your first season? I've borrowed a Petzl Gully with an Aztarex to climb an M4 WI3 (around Scottish V 6 mixed into IV 4 ice) , and the Gully really surprised me at how good it was. For climbing ice it felt totally different to pretty much any other axe I've used- it's so light that you can't let the weight of the axe do the work, but if you swing hard it will bite nicely. For mixed, it was also surprisingly good, but I wasn't going to try torquing it. I immediately bought a Gully afterwards. FWIW my main climbing axes are apexes.
Will a Gully climb well for a couple of mixed routes? Absolutely. Will it survive multiple seasons of regular mixed? I wouldn't bet on it. I'd think of it as high performance in all aspects, but will only last if used sparingly. In other words, it's no work-horse. There will also be techniques that won't be available to you, like stein pulls and torquing.
I haven't tried the Blue Ice. I don't think the venom is as nice a tool as the Gully personally, but it does tick a lot of boxes and the replaceable pick is a huge bonus.
If you really are on a budget, if I were you I'd pick up a pair of cheap second-hand climbing axes and get a gully for ski mountaineering/ alpinism/ light use if you can afford it. A brand new pair of quarks would also be a great option, though I suspect more expensive than my other suggestion.