LHA, ARJ and PKZIP 2.x are based on the same ideas and perform similar (all are based on a huffman encoding of the output of a LZ77 compressor with a sliding window. The window size is around 32 kilobytes). It might be a good idea to look at all of them to experience the command line interface, or the effect of a central directory at the end of file (PKZIP has it, ARJ and LHA don't). RAR is a step upwards, implementing pre-processing of x86 code and uncompressed media contents (WAV, BMP, ...) to improve compression, supporting "solid archives", supporting error recovery data to counteract failing floppies just to name a few technological advantages that made RAR beat the established #1 PKZIP and it's #2 counterpart ARJ. I'm not implying that the technologies implemented in RAR were implemented nowhere before (in contrary: .tar.gz is way older than RAR, and also provides a "solid archive"), but RAR managed to bring these techniques to DOS users in a convenient and easy to use fashion.
If we are looking for something that beats RAR in terms of compression ratio at the expense of speed, and still is 16-bit DOS software, we would need to investigate niche applications. I remember having heard of a compression program called X00, which already is a 32-bit DOS extender based compressor and I am unable to quickly find any good references. This captures a common pattern: If you want better compression, using more memory is a good way to achieve it, and RAR is already at the limit of what you can do in 16 bit DOS software. You would need drastically better algorithms to beat RAR as 16-bit DOS software, and those algorithms turn out to be too slow for DOS machines.
On the other hand, if speed and simplificity of the algorithm would be the main focus, a look at the LZO algorithm and the UCL compression library in UPX.