It seems that the latest improvement in mapping RNA-Seq is Kallisto
kallisto is a program for quantifying abundances of transcripts from RNA-Seq data, or more generally of target sequences using high-throughput sequencing reads. It is based on the novel idea of pseudoalignment for rapidly determining the compatibility of reads with targets, without the need for alignment. On benchmarks with standard RNA-Seq data, kallisto can quantify 30 million human reads in less than 3 minutes on a Mac desktop computer using only the read sequences and a transcriptome index that itself takes less than 10 minutes to build. Pseudoalignment of reads preserves the key information needed for quantification, and kallisto is therefore not only fast, but also as accurate as existing quantification tools. In fact, because the pseudoalignment procedure is robust to errors in the reads, in many benchmarks kallisto significantly outperforms existing tools
BBMap and Seal can directly output FPKMs and coverage when mapping to a transcriptome. BBMap uses more memory than Tophat, but Seal's memory usage is adjustable (tradeoff with sensitivity) using the "rskip" flag. It's extremely fast.
If you determine the differentially expressed transcripts after de novo transcriptome assembly, I recommend to you using "Corset: enabling differential gene expression analysis for de novo assembled transcriptomes". By obtaining the RNA-Seq count data, you can try any of package; DeSeq2, edgeR, limma, boom, etc.
Both of softwares were not used for DEG analysis. Tophat was an aligner software and always used to align reads to reference genome. Trinity was a software platform which used in RNA-seq analysis without reference genome by combining any useful softwares such as bowtie, RSEM, etc. In RNA-seq analysis with reference genome, cufflinks always used to calculate FPKM values of specific genes or isoforms and some R packages such as bioconductor were used in DEG analysis based on known FPKM values; In RNA-seq analysis without reference genome, RSEM and exPress were used to calculate FPKM values and some R packages were used in DEG analysis. I hope these things can help you.