Much cheaper than pills? Seeing how cheap the pills are, I don't think there can be such a big difference. I mean, my pills are about 1.05 $ each before insurance... Given the needles to buy and all, are injections really cheaper? And even if they are, are they worth the huge hassle?
Anyway, I advise against injections, personally. They're painful and hard to do - well, it does depend on the person - and every serious text I have read about them said they did sub-optimal results. As far as I know, they bring faster results, since it's directly into the bloodstream and the dose gets very high very fast, but it makes hormone levels fluctuate a lot between injections.
There is no proof, but since that's not how bodies work (hormones are normally released in a somewhat steady manner, not a big rush once a week), I fully agree with the doctors who think it wouldn't bring as much results in the long term.
The variations can also be unhealthy, I think, for a few reasons I don't know. The fact injectables are not allowed in quite a few countries feels like it supports the idea, too.
Finally, I don't know about you, but I am much less likely to forget a daily habit of taking pills with my breakfast - especially since I have the antiandrogen that's a pill anyway next to it - than an injection once a week. Injection that might even require a visit to a health professional every time, I don't know (but I would personally never trust myself with a delicate thing like an injection!)