Honestly, I haven't done a comparison of the two (but is something I'm highly interested in). This paper - https://science.sciencemag.org/content/360/6390/800 - performs differential expression using SLAM-seq rather than RNA-seq. Haven't read it in detail, but would be interesting to compare the insights gleaned from this paper to previous ones that relied on mRNA-seq.

For now, I can only speak theoretically: RNA-seq gives steady state RNA levels while SLAM-seq gives newly synthesized RNAs (which are metabolically labeled). So a treatment condition that changes the rate of production of certain RNAs: SLAM-seq may more sensitively detect this change than RNA-seq, especially at early time points after the treatment. Also, there's the kinetics aspect: you can infer RNA production/degradation rates in time course experiments. You can figure out if a treatment is decreasing RNA production or is increasing RNA degradation.

Some more insights here: https://www.lexogen.com/slamseq-metabolic-rna-labeling/