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I'm not sure you can compare them like for like and say one is comprehensively better than the other. They have similar sized sensors and similar wide angle focal lengths and apertures but if you need something small, the ZS7 will almost certainly be more suitable but if you like something to wrap your fingers around or you need a long reach for distant subjects, the ZS7 perhaps cannot compete with the S3400. There's also the case of using the camera itself, which is a very personal preference.
My mum has the predecessor to the S3400 (S2950) and I've found it quite usable indoors and for landscape so if the S3400 has been improved in general, I don't think you can go wrong for the money. With that said, I'm not saying you should buy it instead of the ZS7 - you ought to try both out and decide for yourself if possible.
_________________ Bodies: Canon EOS 550D w/ Magic Lantern Lenses: Tokina AT-X 116 Pro DX f/2.8, Canon EF-S 15-85mm f/3.5-5.6 IS USM, Canon EF-S 18-55mm f/3.5-5.6 IS, Canon EF 50mm f/1.8 II, Canon EF 70-300mm f/4-5.6 IS USM Accessories: YongNuo Speedlite YN-468 Flash, Neewer Macro LED Ring Light, Meike Battery Grip, YongNuo RF-602 Wireless Flash Trigger & Receiver YongNuo WR-128 Wireless Remote Control

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