Injections are a hassle, but they're easier on your liver, because they bypass it and go directly into the bloodstream.
That said, the risk of liver inflammation is pretty low anyway, even with pills. It's one of the reasons you do frequent blood tests and the main reason why no one should do unsupervised hormone therapy; if there's any sign of a stressed liver, they can alter your dosage. I don't know what the price of injections is compared to pills, though. I'd imagine injections are cheaper, but don't quote me on that.
If you're worried about your liver health, eat lots of milk thistle supplements.

But, really, tons of people take estradiol pills without issue. Side effects are rather rare.