No. The shift-reduce parser from Stanford is a new implementation which is fast and accurate, much faster than and almost as accurate as the RNN parser, which is the most accurate parser that Stanford has. If you want speed, you might choose the shift-reduce parser. If you need ultimate accuracy, you would not.

Complexity is another matter. Almost all parsers are going to be linear in the number of sentences processed. Technically, it is possible for a parser to beat this, if it processes a large number of sentences at the same time, and shares effort between similar sentences. A group at Berkeley has used this to make very fast parsers that work on GPUs. To do this they have to do heroic amounts of preprocessing of the sentences.

In general, chart parsers have a complexity O(n^3) where n is the number of words in the sentence. This is the worst case, but it rarely comes up with real grammars. There is also a dependence on the size of the grammar. If the grammar is very big, this is important. The standard chart parser will always find all parses allowed by the grammar. That comes at a cost.

The shift-reduce parser is different from chart parsers, and uses heuristics to guide the search for a parse, at the expense of perhaps missing some high-scoring parses. The algorithm uses many fewer steps than the chart parser (linear in the number of words), but each step is potentially quite costly. In practice, it turns out that shift-reduce and other transition-based parsers are fast. But I think that the difference in asymptotic complexity is only part of the reason for this. Much more important is that people, including John Bauer from Stanford, have become very good at implementing them efficiently.