Do whatever's best for you. If you're honest about the whole thing it shouldn't burn a bridge, but there's lots of petty people out there and it might.
If you take job 1 then job 2 becomes a better offer take that one. No one else is going to look out for you and you have nothing to gain by not pursuing a better opportunity except to save a company's feelings which will not benefit you at all.
In my experience as a supervisor I've had tons of people leave for other opportunities and it's only ever pissed me off if they give 0 notice, like walk out that day.
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