These can't be more different. Sevilla is a beautiful city that summarizes the "quintessential typical topic Spain", so perfect if you are looking for a truly Spanish experience. Bilbao is not only the Guggenheim but a fine city where you can experience the Basque food and culture (that some will say its not Spanish, but precisely for that reason not less interesting).
I will not dare to say which one is better because both are two of my favorite cities for very different reasons. but mostly because what's better for me, may be worse for you. To be honest, if I had to choose a city in the North it will probably be San Sebastián with a daytrip to Bilbao. And if I had to choose a city in the South, Granada would win over Sevilla... But these are not the ones you're asking about ;)
Read a bit more about each one and decide which one appeals more to *you*
I doubt budget is a factor. You can get return flights to Bilbao for 80€ or less if you bought your tickets in advance, this is about the same price than a fast AVE train from Madrid to Sevilla (a cheaper slower train, if this exist, or bus, will take about 5 hours too, distances are similar)
Whatever you decide, it's a win-win situation. Have a great trip!
I would choose Seville, a beautiful Andalusian city with plenty of charm. You can see the Cathedral, Giralda Tower, and the Alcazar for starters. Read the top questions in the Seville forum for what to see. Seville is much larger than Bilbao.
A very good hotel where I stay in is the Hotel Becquer, walking distance to most sights.
For train travel:
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