相比之下【xiāngbǐ zhīxià】

相比之下 sets a second thing against one just described: "by comparison", "in contrast". The first clause describes A; 相比之下 opens the next clause, which describes B in the light of A. 之 is a written "it" pointing back at A, so nothing follows 相比之下 except the comma.

The second clause usually carries a degree word – 多了, 得多, 一些, 更 – because the comparison has been set up already.

No object after it

相比之下 already contains its comparison. To name what you're comparing with, use 和…相比 or 与…相比 instead.

• × 相比之下北京，上海更暖和 → 和北京相比，上海更暖和
• × 上海相比之下北京更暖和 → 北京很冷，相比之下，上海更暖和

It is neutral to written, and works in speech too when you're weighing two options.