I've never done either personally, but I have priced out having uBreakiFix replace it and I think they charge $80. According to AccuBattery Pro my battery health is at 91% so not too sure how much more life a replacement battery would get me. (Plus, support for the Pixel 3 likely going to be done in 8 months so not sure it's worth it in that regard either).
If it requires having to use heat to break up glued components, or if you have to remove the display to get the battery, then leave it to the pros. $80 is not a bad price, considering that includes the cost of the battery.